Tanh-sinh quadrature is a method for numerical integration introduced by Hidetoshi Takahashi and Masatake Mori in 1974.
, the integral is approximated by the sum with the abscissas and the weights The Tanh-Sinh method is quite insensitive to endpoint behavior.
This results in a great enhancement of the accuracy of the numerical integration procedure, which is typically performed by the Trapezoidal rule.
In most cases, the transformed integrand displays a rapid roll-off (decay), enabling the numerical integrator to quickly achieve convergence.
In summary, the Tanh-Sinh quadrature scheme is designed so that it gives the most accurate result for the minimum number of function evaluations.